The state Department of Revenue, already under fire for a data breach of sensitive tax information, acknowledged Thursday that it has failed to deliver timely child support payments to about 1,500 parents in Massachusetts since the beginning of the year.

Revenue officials blamed the problem on a faulty computer system implemented in January and said it affected only a tiny percentage of the state’s 160,000 child support recipients. The Baker administration vowed to have the problem mostly fixed by this weekend.

But union officials who represent revenue workers say the issues appear more widespread than the department acknowledges and have disproportionately affected poor parents, many of them single mothers, who are struggling without the child support they are owed.

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The breakdown has also affected another group of parents, mostly fathers, who are having far larger amounts than they are obligated to pay for child support garnished from their unemployment checks, according to officials at SEIU Local 509.

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That issue affected about 1,200 parents who don’t have custody of their kids this year, revenue officials said.

In a statement Thursday, Christopher C. Harding, the revenue commissioner, acknowledged problems with the child support system, saying there have been “some issues affecting less than 1 percent of payments to custodial parents.” He said the agency “anticipates resolving the vast majority of issues around outgoing payments by this weekend.”

Harding added that the Department of Revenue “apologizes to any customers who have been inconvenienced as we transition to the new system.”

Union officials said the Baker administration is underplaying the severity of the problem.

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“The agency claims that 99 percent of cases aren’t affected by glitches,” said Dave Foley, a child support enforcement specialist at the Department of Revenue who serves as chapter president of the agency’s union. “That could be true. But that 1 percent happens to be the most vulnerable population in the state — people who are on unemployment or welfare.”

The problems affecting child support recipients began in early January, when the department launched a new computer system built by Accenture, according to Foley and confirmed by the state.

The state has paid the company more than $19 million for child support enforcement since 2015, according to state records. Accenture referred questions to state revenue officials.

Foley said the problems with the system have not been fixed, leaving front-line employees in the dark about what steps are being taken to remedy the breakdown.

This year’s glitches, Foley said, are affecting low-income parents, primarily mothers, who have had their child support payments pocketed by the state when they go on welfare, in accordance with state policy. They are eligible to resume collecting child support when they leave the welfare rolls.

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But the parents have been not been getting the child support checks they are owed because the computer systems at the Department of Revenue and the Department of Transitional Assistance, which oversees welfare, are not communicating properly, union officials said.

The child support payment issue marks the second serious misstep at the Department of Revenue this year.

Peter MacKinnon, president of Service Employees International Union Local 509, said he has received e-mails from 100 revenue department workers “overwhelmed with people coming to the offices” to complain about not getting child support after they get off welfare.

“Our concern is . . . that people aren’t getting their money,” MacKinnon said. “At the end of the day, we can bemoan a lousy computer system that needs to be fixed, but this is about families needing income to be able to take care of their kids, and we have a system where people aren’t getting what is owed to them, and that’s not OK.”

The other issue affects parents, mostly fathers, who have their child support payments garnished from their unemployment checks.

DOR’s computer system has been mixing up how much these parents owe in child support per week versus what they owe per month, Foley said. A father, for example, who owed $433 a month in child support was instead having $433 per week garnished from his unemployment check, Foley said.

A group of DOR employees have created a workaround system to individually review unemployment checks for errors so the problem “is winding down,” Foley said. But the revenue department’s computer system still isn’t processing the checks automatically, he said.

State officials said the issue with the state accidentally taking too much out of unemployment assistance checks affected about 1,200 noncustodial parents — those who owed child support — and about 800 custodial parents — those receiving it. That pool of 800 parents is part of the broader population of 1,500 parents who haven’t been getting timely child support, officials said, not in addition to it.

The union’s decision to go public with the problem is notable because SEIU Local 509, unlike some other labor groups, has had a close working relationship with Governor Charlie Baker. The governor mentioned MacKinnon and the union by name in his 2016 State of the Commonwealth address, praising both for helping to overhaul the troubled Department of Children and Families. The union represents a total of 20,000 workers, including 8,300 state employees in a variety of human services, health, and education agencies.

Baker is heading into a reelection fight this fall, in which he is expected to campaign heavily on his careful stewardship of state agencies, among other issues.

The child support payment issue marks the second serious misstep at the Department of Revenue this year.

A data breach that made private information from about 39,000 business taxpayers visible to other companies, potentially including competitors, lasted from early August through Jan. 23, the agency has said.

Last month, state revenue officials acknowledged that they had been alerted to the data breach months before fixing the problem, a shift from their initial claim that the problem was fixed hours after it was discovered.

The Department of Revenue is led by Harding, a former business executive. After serving as the agency’s chief of staff, Harding was appointed commissioner by Baker over the summer, and took the reins of the agency in August.

Harding succeeded Michael J. Heffernan who became Baker’s top budget official. Heffernan leads the Executive Office for Administration and Finance, and oversees DOR.